这位中国留英数学专业的小伙子有很好的口才: 数学之美, 他的数学遗憾。
华威大学（The University of Warwick)，famous for mathematics in UK.
Einstein用 Riemann Geometry 数学救了Newton 物理。
3位大师救近代中国数学: 华罗庚, 陈省身, 苏步青
数学光明的未来: AI, Big Data, Cloud Computing
时代的”指数” exponential快脚步, 不要追风, 要一以贯之 : Prof. Andrew Wiles proved 350-year-old “Fermat’s Last Theorem” (FLT).
[纠正]: Andrew Wiles 超过40岁, 没赶上Fields Medal, 只得个”奖励”。他看到椭圆(Ellipse)气球, 得到突破 FLT “工具”的灵感 – “Elliptic Curve” 。
数学是什么: 爱情, 艺术, 音乐, 科技
A self-study Russian mathematician, kicked out 3 times in high schools, expelled from Moscow University, all because he did not attend classes, preferred to self-study in a broader scope for his curiosity, at his own faster speed than the rigid curriculum and boring test-and-exams regime in classrooms.
He did the PhD in Harvard by invitation even he did not have a Bachelor degree, and he barely passed the Harvard’s QE (Qualifying Exams) in Algebraic Geometry, a field in which he made a revolutionary discovery few years later, and for which he was awarded the highest honor : Fields Medal.
This is the typical trait of the geniuses like Evariste Galois, Albert Einstein, Ramanujian, Hua Luogeng (华罗庚), Zhang YiTang (张益唐 – proved “70m Twin Prime Gap”) [#] , Chen Jingrun (陈景润, proved Goldbach Conjecture “1+2”) [##]… with self-motivated curiosity in their field of passion, with reading from the Masters’ works by themselves, PLUS thinking on a problem over many years with perseverance, they finally made great discoveries !
- Topology 拓扑
- Algebraic Geometry 代数几何: Geometry and Algebraic Equations
- Motif: Grothendieck
- Homotopy Theory 同伦
[Full Article] :
[#] : https://tomcircle.wordpress.com/2014/03/01/gaps-between-primes-zhang-yitang/
[##] : https://tomcircle.wordpress.com/2015/07/24/goldbach-conjecture-theorem-chen/
Many excellent Math students after leaving universities more than 10 years forget 90% of math they learned, save some primary school arithmetics – few could do Singapore PSLE Modelling Math or solve quadratic equations.
The “Story-Telling” memory technique via “Signposts” can be used to reconstruct math from first principles:
Note: Lewis Carroll: the author of “Alice in wonderland”
Cambridge Professor Tim Gowers (Fields Medalist) suggested the similar pedagogy of “Memorise by First Principles”.
What is Math ? Interesting article below:
- Mathematics = “that which is learned“ –(Pythagoras)
Math is not about calculation, it is understanding the nature, the universe, the philosophy (logic, intelligence – both “human” and “artificial”)…
What is Axiom, Lemma, Proposition ? Why rigorous Calculus was needed hundred years after Newton & Leibniz had invented it – “Epsilon-Delta” Analysis.
Difference between Riemann Integral & Lebesgue Integral ?
Case “=” : if (a, b) independent
Case “>” : if (a, b) dependent
Thomas Royen used only high-school math (function, derivative) in his proof in 2014. He then published it in arxiv.org website – like Perelman did with the “Poincaré Conjecture”.